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A002840 Number of polyhedral graphs with n edges.
(Formerly M0339 N0129)
1, 0, 1, 2, 2, 4, 12, 22, 58, 158, 448, 1342, 4199, 13384, 43708, 144810, 485704, 1645576, 5623571, 19358410, 67078828, 233800162, 819267086, 2884908430, 10204782956, 36249143676, 129267865144, 462669746182, 1661652306539, 5986979643542 (list; graph; refs; listen; history; text; internal format)



M. B. Dillencourt, Polyhedra of small orders and their Hamiltonian properties. Tech. Rep. 92-91, Info. and Comp. Sci. Dept., Univ. Calif. Irvine, 1992.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. R. S. Walsh, personal communication.


Table of n, a(n) for n=6..35.

C. J. Bouwkamp & N. J. A. Sloane, Correspondence, 1971

A. J. W. Duijvestijn and P. J. Federico, The number of polyhedral (3-connected planar) graphs, Math. Comp. 37 (1981), no. 156, 523-532.

P. J. Federico, Enumeration of polyhedra: the number of 9-hedra, J. Combin. Theory, 7 (1969), 155-161.

G. P. Michon, Counting Polyhedra - Numericana

Hugo Pfoertner, Unlabeled 3-connected planar graphs for n<=20 edges, list in PARI-readable format.

Eric Weisstein's World of Mathematics, Polyhedral Graph

T. R. S. Walsh, Number of sensed planar maps with n edges and m vertices


(PARI) \\ It is assumed that the 3cp.gp file (from the linked zip archive) has been read before, i.e., \r [path]3cp.gp

for(k=6, #ThreeConnectedData, print1(#ThreeConnectedData[k], ", "));

\\ printing of the edge lists of the graphs for n <= 11

print(ThreeConnectedData[6..11]) \\ Hugo Pfoertner, Feb 14 2021


Column sums of A049337.

Cf. A002841, A000944, A046091, A338511, A343869, A343871.

Sequence in context: A112362 A134720 A019225 * A298477 A253677 A182894

Adjacent sequences:  A002837 A002838 A002839 * A002841 A002842 A002843




N. J. A. Sloane


a(30)-a(35) from the Numericana link added by Andrey Zabolotskiy, Jun 13 2020



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Last modified May 25 09:16 EDT 2022. Contains 354066 sequences. (Running on oeis4.)